This invention relates generally to electronic mini-calculators, and more particularly to a hand-held or desk calculator adapted to assist children in acquiring the rudiments of arithmetic, the calculator being capable of performing addition and subtraction of positive integers and of visually displaying computations carried out by the student in a blackboard format.
The value of mini-calculators as a teaching aid is no longer in serious dispute. Thus the National Council of Teachers of Mathematics recently urged teachers to "recognize the potential contribution of the calculator as a valuable instructional aid." This advice is included in a policy statement issued by the National Council to accompany an article on the use of electronic calculators published in the January 1976 issue of The Arithmetic Teacher as well as in The Mathematics Teacher, magazines for elementary and secondary school teachers.
But there are sharp differences of opinion among educators regarding the age level at which the use of electronic calculators should be encouraged. According to the "About Education" column in the Dec. 24, 1975 issue of The New York Times, Dr. E. G. Gibb, President of the National Council, is wary of bringing in the mini-calculator before the fourth grade, for he feels that "the calculator should not be used until the youngster has an understanding of what the calculator is doing for him."
George Grossman, who heads the Mathematics Bureau of the New York City School System, also feels that electronic calculators can be especially valuable in kindling interest in mathematics. Yet, according to the same New York Times column, he suggests that its use not be introduced until the seventh grade.
Thus while teachers of elementary mathematics now appreciate the fact that electronic calculators reinforce the learning of basic numbers and serve to verify the results of pencil and paper computations, they are nevertheless fearful of introducing the calculator at too early an age. Presumably, the beginning student is expected to learn arithmetic by way of the traditional blackboard or pencil and paper technique and should be denied access to calculators in the early phases of instruction.
The apparent contradiction between the recognized value of the electronic calculator as a useful teaching tool and the withholding of this tool until the student has been subjected to several years of traditional instruction is not to be imputed to the resistance of teachers to innovation, but rather to the limitations of existing types of calculators.
To illustrate these limitations, we shall, by way of example, assume that a student is called upon by his teacher to add the numbers 24 and 19 at the blackboard. The student will set up the problem and give the result in the following classic manner:
______________________________________ 24 + 19 = 43 ______________________________________
If now this student is asked to carry out the same computation by means of a standard mini-calculator to verify his result, he will first manipulate the keyboard digits to enter the number 24 which will be displayed on the read out. This read-out usually is in the form of a row of light-emitting diode stations. Before entering the next number, the student will press the + function key, but this operation is not indicated on the display which continues to exhibit number 24. Then he will key in the number 19 which will be displayed in place of 24. To obtain the result, the student thereafter presses the = function key, causing erasure of number 19 and the display of the result 43, thereby verifying the blackboard computation.
A standard mini-calculator which behaves in this fashion is useful to the student who has already acquired a fair degree of proficiency in arithmetic, for he understands that the calculator is carrying out within its internal system the same computation performed on the blackboard, even though this fact is not visible on the display. But for a beginner who is, say, no more than 5 years old and who has yet to grasp the simple concepts underlying arithmetic, the behavior of the conventional calculator is altogether mystifying, in that it fails to display the various numbers being manipulated and the nature of the manipulation, but merely exhibits, at any one time, a single number. As a consequence, educators, while appreciative of the value of mini-calculators for more advanced students, have advised against their use by beginners.
But the fact remains that the first steps in any educational process, whether in reading, writing or arithmetic, are the most crucial, in that these steps psychologically condition the student's attitude toward the subject. If, in his earliest experience with a given subject, a young student is frustrated or blocked in his ability to grasp fundamental principles, this may prejudice his attitude toward the subject and impair his ability to acquire proficiency therein.
It is for this reason that so much attention is now being paid by parents and educators to the kindergarten or pre-school years, for if play and learning can be so intermingled as to implant basic information or skills in the course of participating in a game or carrying out some form of enjoyable activity, this can provide an invaluable introduction to a given subject. While existing types of mini-calculators have value in motivating a student of arithmetic and in reinforcing learning, their limitations are such as to preclude their use in the pre-school years where the need for a playful instructional aid is greatest.